As Israeli and Palestinian negotiators prepare for preliminary talks in Washington on Monday, the future of Jerusalem looms as the thorniest and most difficult issue to resolve.

The State Department announced Sunday that the two sides had accepted invitations from Secretary of State John Kerry to come to Washington "to formally resume direct final status negotiations." The department said two days of initial meetings will begin Monday evening.

U.S. officials say Secretary of State John Kerry will name former U.S. ambassador to Israel Martin Indyk to shepherd the peace talks. The officials, who spoke on condition of anonymity because they were not authorized to speak publicly before the announcement, say Kerry would name Indyk Monday at the State Department.

Kerry's announcement of negotiations came shortly after Israeli Prime Minister Benjamin Netanyahu's Cabinet approved the release of 104 Palestinian prisoners, a key part of the Kerry-brokered deal.

Netanyahu has said Jerusalem — which Israel unified in the 1967 Six-Day War and claims as its capital — is the heart of the Jewish nation and will never be divided.

Palestinian Authority President Mahmoud Abbas says there can be no agreement and no end to the conflict between Palestinians and Israelis without a Palestinian capital in East Jerusalem, home to the Al-Aqsa Mosque, the last remnants of the Jews' Second Temple and the Church of the Holy Sepulcher.

"Jerusalem will be a huge problem" to overcome for any final agreement, says Aaron David Miller, a former adviser on Arab-Israeli peace negotiations to Democratic and Republican secretaries of State. "Down the road, (talks) will fail if Jerusalem is not resolved."

Miller says the parties will tackle other issues first, such as borders and security, to build trust and confidence on both sides before moving to more difficult "identity issues" such as Jerusalem, Palestinian refugees and a demand by Netanyahu that Palestinians recognize Israel as a Jewish homeland.

Before announcing that Israeli and Palestinian leaders agreed to meet on resuming talks, Kerry obtained a pledge from Qatar that it would sweeten an Arab proposal initially put forward by Saudi Arabia in 2002 that offered Israel peace with 22 Arab nations and 35 Muslim nations if it returned all lands it seized in 1967 and agreed to a "just solution" for Palestinian refugees.

Under Qatar's new proposal, the Gulf state said border disputes between Israelis and Palestinians could be solved through land swaps. The Qatari statement meant that Arab states would endorse a compromise on Jewish settlements in the West Bank.

In the 46 years since Israel took control of the land there, it has built Jewish neighborhoods in and around East Jerusalem, and cities in the West Bank that Netanyahu and previous Israeli leaders have pledged to retain in any future deal. How much of the West Bank Israel would retain is yet to be decided, but Israel is expected to compensate Palestinians with territory from territory that was considered part of Israel before 1967, Miller says.

Palestinian women take part in Friday prayers during the holy Muslim month of Ramadan at Al-Aqsa Mosque compound in Jerusalem on July 19.(Photo: Ahmad Gharabli, AFP/Getty Images)

The two sides will also have to agree on security, including what kinds of weapons a Palestinian military would be allowed to have, whether a new Palestinian state could sign defense treaties with other nations and whether Israel could maintain its military presence in the Jordan River Valley, which separates the West Bank from Jordan.

Hussein Ibish, a senior fellow at the American Task Force on Palestine, predicts agreement on such issues is achievable because security is a prerequisite for economic development and is in the Palestinians' self-interest. However, compromise on the fate of hundreds of thousands of Palestinian refugees scattered across the Arab world and on the Palestinian claim to Jerusalem will be much harder, Ibish says.

Ibish says Palestinians will have to accept that refugees and their descendants who've lived for decades without full citizenship in other nations will never be allowed to return to the homes they left. Their numbers would outnumber the Jewish population, which Israel would never accept, Ibish says.

On Jerusalem, however, there will either be a compromise or no deal, he says.

Competing claims on the land are most intense in the Temple Mount-Haram al Sharif area and the stone-paved 1-square-kilometer area of Jerusalem's Old City. But Jewish neighborhoods and construction in and around East Jerusalem have given rise to various creative solutions for resolving the riddle of how two people can share the same place:

• Palestine or Israel could have exclusive sovereignty over individual areas of the Holy Basin and the Old City. However, Ibish says such an option is not viable because neither side will trust the other, and the city has to somehow operate as a municipality with shared transportation, electrical grid and other services.

• Another option is shared sovereignty or some kind of international administration for the Holy Basin, where it would be managed by a United Nations committee headed by a party agreed to by both sides.

• A light-rail system along the border of Israel and the West Bank boundary of the new Palestine could include train stops that would incorporate border crossings from one side to another. A sketch of this notion was reportedly put on the table during 2008 negotiations between Abbas and then-Israeli Prime Minister Ehud Olmert.

Edward Djerejian, U.S. ambassador to Israel from 1992 to 1995 under President Clinton, has made fresh proposals of his own as director of the James A. Baker III Institute for Public Policy at Rice University in Texas. The two sides will have to agree upon a unified city that serves as a capital for two states and has joint municipal planning for shared systems such as the electrical grid and transportation, Djerejian says.

"At the end of the day, it is going to be intermingled in many ways," and it would be a first arrangement of its kind in the world, he says. "I can't think of another city where that pertains."